The specific resistance of single-crystal semiconductor changes upon pressures or forces thereon resulting in strains within the semiconductor element. This is known as the piezo-resistive effect. With respect to the crystal, the effect is anisotropic, that is, it depends on the direction of the forces with respect to the respective planes of the crystal, typically a silicon crystal, and with the respect to the direction of current flow in the crystal element which form resistances, the resistance of which varies in accordance with the strain within the semiconductor itself. Various types of pressure sensors, force sensors, acceleration sensors, and the like, operating on the basis of this principle are known. The piezo-resistive resistance elements can be located in various crystal planes of the silicon crystal. The particular location of the resistance with respect to the crystal plane has respective advantages and disadvantages in application. Preferred crystal planes for the resistances are the (111)-plane, the (110)-plane, and the (001)-plane.
To determine the change in resistance upon change in strain within the semiconductor material, that is, to determine applied pressure, force or other parameter acting on the crystal, it has been proposed to include the resistance of the crystal in a bridge network. All, or at least a portion of the resistances of the bridge network, can be placed on an elastic support which, to measure pressure, can be formed as a membrane. Various shapes of such a membrane have been proposed. Either circular or rectangular membranes are preferred. Upon application of pressure to a circular membrane, the mechanical strain therein depends on the distance from the center of the membrane. The mechanical strain at the center of the membrane is the same for all directions. To measure applied pressure, it is thus necessary to locate the resistances on a circular membrane unsymmetrically or eccentrically with respect thereto, so that the different resistance branches of the bridge will have different resistances and will have different resistance changes upon application of pressure which do not compensate to zero. This arrangement leads to problems with linearity of the piezo-resistive resistance bridge and to undesired offset voltages of the electric output signal obtained from the pressure sensor system. One of the advantages of an arrangement with a circular membrane is the relative ease of exact reproducibility of the circular membrane itself.
Rectangular membranes have advantages and disadvantages with respect to the circular membrane; they are more suitable to obtain measurements since the mechanical strain in the longitudinal and transverse direction may be substantially different. A square resistance bridge can thus be located in the center of a rectangular membrane, thus improving the linearity and offset characteristics of the overall piezo-resistive devices. In dependence on the manufacturing process of the membrane, however, the accuracy of exact reproduction is poor. The membrane is usually made by etching. Consequently, there is a wide difference in characteristics of membranes which should be identical, and the tolerance variation in response and sensitivity of theoretically similar devices is wide. Rectangular membranes further are subject to increased mechanical stresses at the edges and the corners of the membrane and fracture of the membrane at those points is a frequently recurring problem.